International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 6, Pages 937-948
doi:10.1155/IJMMS.2005.937

A survey of weighted substitution operators and generalizations of Banach--Stone theorem

Abstract

The classical Banach-Stone theorem characterizes linear surjective isometries between C(K)-spaces. The main aim of this paper is to present a survey of Banach-Stone-theorem-type results between some function spaces. The weighted substitution operators play an important role in characterization of isometries, disjointness preserving operators, and lattice homomorphisms. Some open problems are given for further investigation.